In general, numerical analysis of an incompressible fluid and numerical analysis of a compressible fluid are performed by using different fluid analyzing apparatuses or separate fluid analyzing methods.
Although not general, there is a unified analyzing method for an incompressible fluid and a compressible fluid. The unified analyzing method for an incompressible fluid and a compressible fluid are classified by the following three types. A method of the first type extends a solution of an incompressible fluid to make it possible to analyze a compressible fluid. A method of the second type subjects a solution of an incompressible fluid to a preconditioning matrix to make it possible to analyze an incompressible fluid. A method of the third type is an analyzing method which advects a physical quantity by a nonconservative discrete equation as in a CIPCUP (CCUP) method (for example, see CIP introductory, “Simulation Summer School of Celestial Body and Space Plasma” document, Sep. 11 to Sep. 15, 2002) or a QCAM method (for example, see Mikiya AKAMATSU et al., “Computational Method Based On a Quasi-Conservative Formulation for Fluid Flows under Arbitrary Mach Number Condition”, Transactions of the Japan society of mechanical engineers, (Ser. B), Vol. 69, No.682 (June 2003), pp. 1386 to 1393).
The reasons why a unified analyzing method for an incompressible fluid and a compressible fluid is not general are as follows. That is, the method of the first type cannot analyze an unsteady fluid with time developing. The method of the second type depends on nonphysical parameters in a preconditioning matrix. In the method of the third type, an iterative calculation performed in pressure calculation is deteriorated in convergence and makes a calculation load large.
The reason why the convergence of an iterative calculation is deteriorated will be described below. In general, an error caused by a numerical calculation occurs because the number of significant figures of a fluid analyzing apparatus is finite and because a calculation using an iterative solution is terminated at a finite number of times. Since the number of significant figures is finite, when the number of calculations increases, errors caused by a cutoff value following the significant digit are accumulated. In the iterative method, a solution is expected to be converged. However, when the calculation is terminated at a finite number of times, errors occur. These errors deteriorate the convergence of the iterative calculation.
As a patent document which discloses an analyzing method (in which an advection term and a nonadvection term are separated from each other) for advecting physical quantity by a nonconservative discrete equation, Japanese Patent Application Laid-Open No. 2002-312342 (the 62nd and 65th paragraphs FIG. 4, and the like) or the like is known.